Question

3 - 8. the three - dimensional shape at right is called a cylinder. its bottom and top bases are same - sized circles, and its “side” is perpendicular to the bases. what would the shape of a flag need to be in order to generate a cylinder when it spins about its pole? (you may want to refer to problem 3 - 3 to review how flags work.)

Explanation:

Step1: Recall 3 - D shape generation

When a 2 - D shape is rotated about an axis, it can form a 3 - D shape. For a cylinder, we consider the relationship between its cross - section and the generating 2 - D shape.

Step2: Analyze the cylinder's structure

A cylinder has circular bases and a lateral surface. If we spin a rectangle about one of its sides (which can be thought of as the flag - pole), the other side of the rectangle will trace out a circular path, and the rectangle as a whole will generate a cylinder.

Answer:

Rectangle